Analytical solution of rotationally symmetric Stokes flow near corners. (English) Zbl 1340.76025

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 15–17, 2013. In honor of the 70th birthday of Karel Segeth. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-61-5). 13-20 (2013).
An analytical solution of the Stokes problem in 2D domains is presented, which is then used to characterize the singular part of the solution of the Stokes and Navier-Stokes equations near corners on the boundary of the domain. This approach leads to a very precise numerical finite element solution, which is also illustrated on two numerical examples: flow in a channel with forward and backward steps and a lid driven cavity.
For the entire collection see [Zbl 1277.00032].


76D07 Stokes and related (Oseen, etc.) flows
76D05 Navier-Stokes equations for incompressible viscous fluids
76M10 Finite element methods applied to problems in fluid mechanics
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics


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